Assignment 2

Introduction

Aim: Determine if there is a model to conveniently measure body fat percent at home

Data Description

Data Wrangling: BF Percent

Reducing Outliers

Siri equation

\[ Pct.BF = \frac{495}{density} - 450 \]

Wrangling cont.

Incorrect Results

• Body density of the human body typically falls within the range of 0.900 to 1.100 g/cm³ (Jackson & Pollock, 2007)

Exploratory Data Analysis: Scatter plots

Exploratory Data Analysis: Correlation Analysis

Checking Assumptions: Multicollinearity

Checking Assumptions: Homoscedacity and Normality

Residual plots

Stepwise Regression and Stepwise Subset Selection

stepwise_model_backward <- step(lm_model, direction = "backward",
                       trace = 0)

summary(stepwise_model_backward)

Cross Validation and Performance

Generalised Least Squares: Residual Analysis

AIC:  1484.033  BIC:  1535.927  Residual standard error: 4.341277

Generalised Least Squares: Performance Analysis

Derived Variables

• We would also like to investigate the effectiveness of using common measurements derived from the variables in our models

Body Mass Index (BMI) where:

\[ \text{BMI} = \frac{\text{Weight(lb)}}{\text{Height(inches)}} \cdot 703 \]

Waist-Hip Ratio (WHR) where:

\[ \text{WHR} = \frac{\text{Waist Circumference}}{\text{Hip Circumference}} \]

Exploratory Analysis

Comparing Model Performance